They will examine how a function behaves as the input approaches a particular value. They will estimate limits from graphs, and tables of values. In this activity, the average rate of change between two points is defined and then used as a concept connecting ideas of slope, difference quotients, and approximations of instantaneous rate of change.
In this activity, students will investigate the given function, and state and explain the limit at a particular value. They also state and explain the limit at a particular value from a graph. Students learn to associate the graph of a function with its derivative. In this activity, students explore a graphical feature of some functions called local linearity.
They also investigate the link between local linearity and differentiability through several examples. News Center Contact TI. Manage preferences Agree and Proceed. Control your cookie preferences You can control your preferences for how we use cookies to collect and use information while you're on TI websites by adjusting the status of these categories. These cookies help identify who you are and store your activity and account information in order to deliver enhanced functionality, including a more personalized and relevant experience on our sites.
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Accept all. Standards Textbook. Download Making Limits Exist In this activity, students will graph piecewise functions and evaluate numerically and graphically the left hand limit and the right hand limit of the function as x approaches a given number, c. Graphical Consequences of Continuity Students explore the graphical and numeric consequences of continuity. Download 5, To Infinity and Beyond! Approaching Limits In this activity, students' will investigate, both graphically and numerically, the limit of a function at a point.
Download 4, However, running programs by the built-in methods wastes a lot of memory, so shells were written which have different formats, and load programs in different ways, to avoid wasting memory and provide other features such as libraries for programs. Ion takes about 1. There are also numerous Ion-compatible shells available on ticalc. To install Ion, you must send the supplied group file ION.
Then, you have to run the 'ION' program to install the shell. After it has been installed, run the 'A' program to start Ion. Then select an Ion program from the list that is shown to run it. Most programs for these shells have now been converted to Ion, so in general, if you want to run a program for one of them, you should try to get the Ion version instead which is likely to be better updated. If you have one of the few such programs that doesn't also have an Ion version, you will need to install the appropriate shell on your TI to run them.
The environment for running assembly programs is essentially the same on these two calculators. Virtually all programs written for one will work on the other with no difficulties. Since the Silver Edition has more memory and speed, a program designed to require these features might not work properly or at all on a regular TI Plus.
However, very few if any such programs exist. These calculators do have built-in assembly capability which allows you to run assembly programs directly. However, running programs by the built-in method wastes a lot of memory. Most programs are written for shells which reduces the program's memory use when running, and also provide other features such as libraries for programs.
Developing for Ion has the advantage that you can easily make programs that run on both the TI and the TI Plus calculators and such programs now work on calculators up to the TI Plus Silver Edition. The other shells are Ion-compatible so a program written for Ion can be used even if you have a different shell. However, it is probably a good idea to put the original files in archive so that you can re-install Ion in case your RAM is reset you will need to temporarily unarchive them to re-install Ion.
A newer shell for these calculators is MirageOS , written by Detached Solutions, which is not a regular program, but instead is a flash application. Since it's a flash app it takes 16K of memory instead of only 2K or so like other shells, which may be a problem for the plain TI Plus but probably doesn't matter on the TI Plus Silver Edition or any variety of TI Plus since they have so much storage.
MirageOS can run Ion programs, and has some extra additional features such as a folder-based file manager. It also can run some TI asm programs though this isn't very useful, as most TI programs also have an Ion version.
MirageOS can run Ion programs but also has it own format for programs which will not work on Ion. An even newer shell is Doors CS which is a flash app as well. It can run both Ion and MirageOS programs, and has its own format too. You will need to use Doors CS if you want to run programs specifically written for it. They should be able to run nearly all programs made for the TI Plus.
They should be run in the same way as on the TI Plus see the previous section. Note that if you are using MirageOS, you need at least version 1. There are very few significant assembly programs for either of these calculators which don't use any shell.
Flash applications are similar to asm programs in that they are stored as machine code. However, they have many differences, such as:. To run flash applications on your calculator, press the APPS button to bring up a menu of the installed applications. Then select one to run it. MirageOS does have some support for emulating TI programs.
Even though it is called "AsmComp ", it does not really compile assembly code. These names are actually quite misleading.
The so-called ASCII format contains the program expanded in hexadecimal format as text in a regular program e. To successfully enter as ASM program, you would have to type it in using the "ASCII" format of it, which means that you would have to see the machine code version of it, most likely by assembling it on a computer and viewing the output of the assembler or by examining the assembled version of a program that was already released.
You also could write programs in hex yourself if you had the instruction set table which you can find in ticalc. Apparently in order to prevent unauthorized copying of flash applications, TI added a limit to the size of normal assembly programs, in the form of a hardware device which prevents executing code outside of a certain area. The limit is really a 16K limit; that is, code can be run anywhere within the first 16K of memory. However, part of this area is used for system data; beginning at the normal start address for assembly programs, there is about 8.
This is not an actual limit on the size of a program; programs can work if they are larger than this, as long as the area after the first 8.
Furthermore, the implementation of Ion's libraries makes the problem somewhat worse for Ion users.
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